1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 192,020 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… miss… e380000… nhs_glo…     1 gl34fe   South West
##  2 111       2020-03-18 fema… miss… e380001… nhs_sou…     1 ne325nn  North Eas…
##  3 111       2020-03-18 fema… 0-18  e380000… nhs_air…     8 bd57jr   North Eas…
##  4 111       2020-03-18 fema… 0-18  e380000… nhs_ash…     7 tn254ab  South East
##  5 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  6 111       2020-03-18 fema… 0-18  e380000… nhs_bar…     9 n111np   London    
##  7 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    11 s752py   North Eas…
##  8 111       2020-03-18 fema… 0-18  e380000… nhs_bas…    19 ss143hg  East of E…
##  9 111       2020-03-18 fema… 0-18  e380000… nhs_bas…     6 dn227xf  North Eas…
## 10 111       2020-03-18 fema… 0-18  e380000… nhs_bat…     9 ba25rp   South West
## # … with 192,010 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##      date_report               nhs_region deaths
## 1     2020-03-01          East of England      0
## 2     2020-03-02          East of England      1
## 3     2020-03-03          East of England      0
## 4     2020-03-04          East of England      0
## 5     2020-03-05          East of England      0
## 6     2020-03-06          East of England      1
## 7     2020-03-07          East of England      0
## 8     2020-03-08          East of England      0
## 9     2020-03-09          East of England      1
## 10    2020-03-10          East of England      0
## 11    2020-03-11          East of England      0
## 12    2020-03-12          East of England      0
## 13    2020-03-13          East of England      1
## 14    2020-03-14          East of England      2
## 15    2020-03-15          East of England      2
## 16    2020-03-16          East of England      1
## 17    2020-03-17          East of England      1
## 18    2020-03-18          East of England      5
## 19    2020-03-19          East of England      4
## 20    2020-03-20          East of England      2
## 21    2020-03-21          East of England     11
## 22    2020-03-22          East of England     12
## 23    2020-03-23          East of England     11
## 24    2020-03-24          East of England     19
## 25    2020-03-25          East of England     26
## 26    2020-03-26          East of England     36
## 27    2020-03-27          East of England     38
## 28    2020-03-28          East of England     28
## 29    2020-03-29          East of England     43
## 30    2020-03-30          East of England     45
## 31    2020-03-31          East of England     70
## 32    2020-04-01          East of England     62
## 33    2020-04-02          East of England     65
## 34    2020-04-03          East of England     80
## 35    2020-04-04          East of England     71
## 36    2020-04-05          East of England     76
## 37    2020-04-06          East of England     71
## 38    2020-04-07          East of England     93
## 39    2020-04-08          East of England    111
## 40    2020-04-09          East of England     87
## 41    2020-04-10          East of England     74
## 42    2020-04-11          East of England     92
## 43    2020-04-12          East of England    100
## 44    2020-04-13          East of England     78
## 45    2020-04-14          East of England     61
## 46    2020-04-15          East of England     82
## 47    2020-04-16          East of England     74
## 48    2020-04-17          East of England     86
## 49    2020-04-18          East of England     64
## 50    2020-04-19          East of England     67
## 51    2020-04-20          East of England     67
## 52    2020-04-21          East of England     75
## 53    2020-04-22          East of England     67
## 54    2020-04-23          East of England     49
## 55    2020-04-24          East of England     66
## 56    2020-04-25          East of England     54
## 57    2020-04-26          East of England     48
## 58    2020-04-27          East of England     46
## 59    2020-04-28          East of England     58
## 60    2020-04-29          East of England     32
## 61    2020-04-30          East of England     45
## 62    2020-05-01          East of England     49
## 63    2020-05-02          East of England     29
## 64    2020-05-03          East of England     41
## 65    2020-05-04          East of England     19
## 66    2020-05-05          East of England     36
## 67    2020-05-06          East of England     31
## 68    2020-05-07          East of England     33
## 69    2020-05-08          East of England     33
## 70    2020-05-09          East of England     29
## 71    2020-05-10          East of England     22
## 72    2020-05-11          East of England     18
## 73    2020-05-12          East of England     21
## 74    2020-05-13          East of England     27
## 75    2020-05-14          East of England     26
## 76    2020-05-15          East of England     19
## 77    2020-05-16          East of England     26
## 78    2020-05-17          East of England     17
## 79    2020-05-18          East of England     25
## 80    2020-05-19          East of England     15
## 81    2020-05-20          East of England     26
## 82    2020-05-21          East of England     21
## 83    2020-05-22          East of England     13
## 84    2020-05-23          East of England     12
## 85    2020-05-24          East of England     17
## 86    2020-05-25          East of England     25
## 87    2020-05-26          East of England     14
## 88    2020-05-27          East of England     12
## 89    2020-05-28          East of England     17
## 90    2020-05-29          East of England     16
## 91    2020-05-30          East of England      9
## 92    2020-05-31          East of England      8
## 93    2020-06-01          East of England     17
## 94    2020-06-02          East of England     14
## 95    2020-06-03          East of England     10
## 96    2020-06-04          East of England      7
## 97    2020-06-05          East of England     14
## 98    2020-06-06          East of England      5
## 99    2020-06-07          East of England      9
## 100   2020-06-08          East of England      7
## 101   2020-06-09          East of England      6
## 102   2020-06-10          East of England      8
## 103   2020-06-11          East of England      1
## 104   2020-06-12          East of England      9
## 105   2020-06-13          East of England      5
## 106   2020-06-14          East of England      4
## 107   2020-06-15          East of England      8
## 108   2020-06-16          East of England      3
## 109   2020-06-17          East of England      7
## 110   2020-06-18          East of England      4
## 111   2020-06-19          East of England      7
## 112   2020-06-20          East of England      4
## 113   2020-06-21          East of England      3
## 114   2020-06-22          East of England      6
## 115   2020-06-23          East of England      5
## 116   2020-06-24          East of England      4
## 117   2020-06-25          East of England      1
## 118   2020-06-26          East of England      5
## 119   2020-06-27          East of England      6
## 120   2020-06-28          East of England      8
## 121   2020-06-29          East of England      4
## 122   2020-06-30          East of England      5
## 123   2020-07-01          East of England      2
## 124   2020-07-02          East of England      5
## 125   2020-07-03          East of England      0
## 126   2020-07-04          East of England      3
## 127   2020-07-05          East of England      1
## 128   2020-07-06          East of England      2
## 129   2020-07-07          East of England      2
## 130   2020-07-08          East of England      0
## 131   2020-07-09          East of England      8
## 132   2020-07-10          East of England      4
## 133   2020-07-11          East of England      2
## 134   2020-07-12          East of England      1
## 135   2020-07-13          East of England      7
## 136   2020-07-14          East of England      2
## 137   2020-07-15          East of England      0
## 138   2020-07-16          East of England      0
## 139   2020-07-17          East of England      0
## 140   2020-07-18          East of England      0
## 141   2020-07-19          East of England      1
## 142   2020-07-20          East of England      1
## 143   2020-07-21          East of England      0
## 144   2020-07-22          East of England      1
## 145   2020-07-23          East of England      1
## 146   2020-07-24          East of England      1
## 147   2020-07-25          East of England      0
## 148   2020-07-26          East of England      1
## 149   2020-07-27          East of England      0
## 150   2020-07-28          East of England      0
## 151   2020-03-01                   London      0
## 152   2020-03-02                   London      0
## 153   2020-03-03                   London      0
## 154   2020-03-04                   London      0
## 155   2020-03-05                   London      0
## 156   2020-03-06                   London      1
## 157   2020-03-07                   London      0
## 158   2020-03-08                   London      0
## 159   2020-03-09                   London      1
## 160   2020-03-10                   London      0
## 161   2020-03-11                   London      5
## 162   2020-03-12                   London      6
## 163   2020-03-13                   London     10
## 164   2020-03-14                   London     13
## 165   2020-03-15                   London      9
## 166   2020-03-16                   London     15
## 167   2020-03-17                   London     23
## 168   2020-03-18                   London     27
## 169   2020-03-19                   London     25
## 170   2020-03-20                   London     44
## 171   2020-03-21                   London     49
## 172   2020-03-22                   London     54
## 173   2020-03-23                   London     63
## 174   2020-03-24                   London     86
## 175   2020-03-25                   London    112
## 176   2020-03-26                   London    129
## 177   2020-03-27                   London    129
## 178   2020-03-28                   London    122
## 179   2020-03-29                   London    145
## 180   2020-03-30                   London    149
## 181   2020-03-31                   London    181
## 182   2020-04-01                   London    202
## 183   2020-04-02                   London    191
## 184   2020-04-03                   London    197
## 185   2020-04-04                   London    231
## 186   2020-04-05                   London    195
## 187   2020-04-06                   London    197
## 188   2020-04-07                   London    220
## 189   2020-04-08                   London    239
## 190   2020-04-09                   London    206
## 191   2020-04-10                   London    170
## 192   2020-04-11                   London    178
## 193   2020-04-12                   London    158
## 194   2020-04-13                   London    166
## 195   2020-04-14                   London    143
## 196   2020-04-15                   London    142
## 197   2020-04-16                   London    140
## 198   2020-04-17                   London    100
## 199   2020-04-18                   London    101
## 200   2020-04-19                   London    103
## 201   2020-04-20                   London     96
## 202   2020-04-21                   London     94
## 203   2020-04-22                   London    109
## 204   2020-04-23                   London     77
## 205   2020-04-24                   London     71
## 206   2020-04-25                   London     58
## 207   2020-04-26                   London     53
## 208   2020-04-27                   London     51
## 209   2020-04-28                   London     44
## 210   2020-04-29                   London     45
## 211   2020-04-30                   London     40
## 212   2020-05-01                   London     41
## 213   2020-05-02                   London     41
## 214   2020-05-03                   London     36
## 215   2020-05-04                   London     30
## 216   2020-05-05                   London     25
## 217   2020-05-06                   London     37
## 218   2020-05-07                   London     37
## 219   2020-05-08                   London     30
## 220   2020-05-09                   London     23
## 221   2020-05-10                   London     26
## 222   2020-05-11                   London     18
## 223   2020-05-12                   London     18
## 224   2020-05-13                   London     17
## 225   2020-05-14                   London     20
## 226   2020-05-15                   London     18
## 227   2020-05-16                   London     14
## 228   2020-05-17                   London     15
## 229   2020-05-18                   London     11
## 230   2020-05-19                   London     14
## 231   2020-05-20                   London     19
## 232   2020-05-21                   London     12
## 233   2020-05-22                   London     10
## 234   2020-05-23                   London      6
## 235   2020-05-24                   London      7
## 236   2020-05-25                   London      9
## 237   2020-05-26                   London     14
## 238   2020-05-27                   London      7
## 239   2020-05-28                   London      8
## 240   2020-05-29                   London      7
## 241   2020-05-30                   London     12
## 242   2020-05-31                   London      6
## 243   2020-06-01                   London     10
## 244   2020-06-02                   London      8
## 245   2020-06-03                   London      6
## 246   2020-06-04                   London      8
## 247   2020-06-05                   London      4
## 248   2020-06-06                   London      0
## 249   2020-06-07                   London      5
## 250   2020-06-08                   London      5
## 251   2020-06-09                   London      5
## 252   2020-06-10                   London      8
## 253   2020-06-11                   London      5
## 254   2020-06-12                   London      3
## 255   2020-06-13                   London      3
## 256   2020-06-14                   London      3
## 257   2020-06-15                   London      1
## 258   2020-06-16                   London      2
## 259   2020-06-17                   London      1
## 260   2020-06-18                   London      2
## 261   2020-06-19                   London      5
## 262   2020-06-20                   London      3
## 263   2020-06-21                   London      4
## 264   2020-06-22                   London      2
## 265   2020-06-23                   London      1
## 266   2020-06-24                   London      4
## 267   2020-06-25                   London      3
## 268   2020-06-26                   London      2
## 269   2020-06-27                   London      1
## 270   2020-06-28                   London      2
## 271   2020-06-29                   London      2
## 272   2020-06-30                   London      1
## 273   2020-07-01                   London      2
## 274   2020-07-02                   London      2
## 275   2020-07-03                   London      2
## 276   2020-07-04                   London      1
## 277   2020-07-05                   London      3
## 278   2020-07-06                   London      2
## 279   2020-07-07                   London      1
## 280   2020-07-08                   London      3
## 281   2020-07-09                   London      4
## 282   2020-07-10                   London      0
## 283   2020-07-11                   London      1
## 284   2020-07-12                   London      1
## 285   2020-07-13                   London      1
## 286   2020-07-14                   London      0
## 287   2020-07-15                   London      2
## 288   2020-07-16                   London      0
## 289   2020-07-17                   London      0
## 290   2020-07-18                   London      2
## 291   2020-07-19                   London      0
## 292   2020-07-20                   London      0
## 293   2020-07-21                   London      1
## 294   2020-07-22                   London      0
## 295   2020-07-23                   London      2
## 296   2020-07-24                   London      0
## 297   2020-07-25                   London      1
## 298   2020-07-26                   London      0
## 299   2020-07-27                   London      0
## 300   2020-07-28                   London      0
## 301   2020-03-01                 Midlands      0
## 302   2020-03-02                 Midlands      0
## 303   2020-03-03                 Midlands      1
## 304   2020-03-04                 Midlands      0
## 305   2020-03-05                 Midlands      0
## 306   2020-03-06                 Midlands      0
## 307   2020-03-07                 Midlands      0
## 308   2020-03-08                 Midlands      2
## 309   2020-03-09                 Midlands      1
## 310   2020-03-10                 Midlands      0
## 311   2020-03-11                 Midlands      2
## 312   2020-03-12                 Midlands      6
## 313   2020-03-13                 Midlands      5
## 314   2020-03-14                 Midlands      4
## 315   2020-03-15                 Midlands      5
## 316   2020-03-16                 Midlands     11
## 317   2020-03-17                 Midlands      8
## 318   2020-03-18                 Midlands     13
## 319   2020-03-19                 Midlands      8
## 320   2020-03-20                 Midlands     28
## 321   2020-03-21                 Midlands     13
## 322   2020-03-22                 Midlands     31
## 323   2020-03-23                 Midlands     33
## 324   2020-03-24                 Midlands     41
## 325   2020-03-25                 Midlands     48
## 326   2020-03-26                 Midlands     64
## 327   2020-03-27                 Midlands     72
## 328   2020-03-28                 Midlands     89
## 329   2020-03-29                 Midlands     92
## 330   2020-03-30                 Midlands     90
## 331   2020-03-31                 Midlands    123
## 332   2020-04-01                 Midlands    140
## 333   2020-04-02                 Midlands    142
## 334   2020-04-03                 Midlands    124
## 335   2020-04-04                 Midlands    151
## 336   2020-04-05                 Midlands    164
## 337   2020-04-06                 Midlands    140
## 338   2020-04-07                 Midlands    123
## 339   2020-04-08                 Midlands    186
## 340   2020-04-09                 Midlands    139
## 341   2020-04-10                 Midlands    127
## 342   2020-04-11                 Midlands    142
## 343   2020-04-12                 Midlands    139
## 344   2020-04-13                 Midlands    120
## 345   2020-04-14                 Midlands    116
## 346   2020-04-15                 Midlands    147
## 347   2020-04-16                 Midlands    102
## 348   2020-04-17                 Midlands    118
## 349   2020-04-18                 Midlands    115
## 350   2020-04-19                 Midlands     92
## 351   2020-04-20                 Midlands    107
## 352   2020-04-21                 Midlands     86
## 353   2020-04-22                 Midlands     78
## 354   2020-04-23                 Midlands    103
## 355   2020-04-24                 Midlands     79
## 356   2020-04-25                 Midlands     72
## 357   2020-04-26                 Midlands     81
## 358   2020-04-27                 Midlands     74
## 359   2020-04-28                 Midlands     68
## 360   2020-04-29                 Midlands     53
## 361   2020-04-30                 Midlands     56
## 362   2020-05-01                 Midlands     64
## 363   2020-05-02                 Midlands     51
## 364   2020-05-03                 Midlands     52
## 365   2020-05-04                 Midlands     61
## 366   2020-05-05                 Midlands     59
## 367   2020-05-06                 Midlands     59
## 368   2020-05-07                 Midlands     48
## 369   2020-05-08                 Midlands     34
## 370   2020-05-09                 Midlands     37
## 371   2020-05-10                 Midlands     42
## 372   2020-05-11                 Midlands     33
## 373   2020-05-12                 Midlands     45
## 374   2020-05-13                 Midlands     40
## 375   2020-05-14                 Midlands     38
## 376   2020-05-15                 Midlands     40
## 377   2020-05-16                 Midlands     34
## 378   2020-05-17                 Midlands     31
## 379   2020-05-18                 Midlands     36
## 380   2020-05-19                 Midlands     35
## 381   2020-05-20                 Midlands     36
## 382   2020-05-21                 Midlands     32
## 383   2020-05-22                 Midlands     27
## 384   2020-05-23                 Midlands     34
## 385   2020-05-24                 Midlands     20
## 386   2020-05-25                 Midlands     26
## 387   2020-05-26                 Midlands     33
## 388   2020-05-27                 Midlands     29
## 389   2020-05-28                 Midlands     28
## 390   2020-05-29                 Midlands     20
## 391   2020-05-30                 Midlands     21
## 392   2020-05-31                 Midlands     22
## 393   2020-06-01                 Midlands     20
## 394   2020-06-02                 Midlands     22
## 395   2020-06-03                 Midlands     24
## 396   2020-06-04                 Midlands     16
## 397   2020-06-05                 Midlands     21
## 398   2020-06-06                 Midlands     20
## 399   2020-06-07                 Midlands     17
## 400   2020-06-08                 Midlands     16
## 401   2020-06-09                 Midlands     18
## 402   2020-06-10                 Midlands     15
## 403   2020-06-11                 Midlands     13
## 404   2020-06-12                 Midlands     12
## 405   2020-06-13                 Midlands      6
## 406   2020-06-14                 Midlands     18
## 407   2020-06-15                 Midlands     12
## 408   2020-06-16                 Midlands     15
## 409   2020-06-17                 Midlands     11
## 410   2020-06-18                 Midlands     15
## 411   2020-06-19                 Midlands     10
## 412   2020-06-20                 Midlands     15
## 413   2020-06-21                 Midlands     14
## 414   2020-06-22                 Midlands     14
## 415   2020-06-23                 Midlands     16
## 416   2020-06-24                 Midlands     15
## 417   2020-06-25                 Midlands     18
## 418   2020-06-26                 Midlands      5
## 419   2020-06-27                 Midlands      5
## 420   2020-06-28                 Midlands      7
## 421   2020-06-29                 Midlands      6
## 422   2020-06-30                 Midlands      6
## 423   2020-07-01                 Midlands      7
## 424   2020-07-02                 Midlands      9
## 425   2020-07-03                 Midlands      3
## 426   2020-07-04                 Midlands      4
## 427   2020-07-05                 Midlands      6
## 428   2020-07-06                 Midlands      5
## 429   2020-07-07                 Midlands      3
## 430   2020-07-08                 Midlands      5
## 431   2020-07-09                 Midlands      9
## 432   2020-07-10                 Midlands      3
## 433   2020-07-11                 Midlands      0
## 434   2020-07-12                 Midlands      5
## 435   2020-07-13                 Midlands      1
## 436   2020-07-14                 Midlands      1
## 437   2020-07-15                 Midlands      6
## 438   2020-07-16                 Midlands      2
## 439   2020-07-17                 Midlands      3
## 440   2020-07-18                 Midlands      3
## 441   2020-07-19                 Midlands      3
## 442   2020-07-20                 Midlands      3
## 443   2020-07-21                 Midlands      0
## 444   2020-07-22                 Midlands      2
## 445   2020-07-23                 Midlands      6
## 446   2020-07-24                 Midlands      1
## 447   2020-07-25                 Midlands      3
## 448   2020-07-26                 Midlands      4
## 449   2020-07-27                 Midlands      3
## 450   2020-07-28                 Midlands      0
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## 452   2020-03-02 North East and Yorkshire      0
## 453   2020-03-03 North East and Yorkshire      0
## 454   2020-03-04 North East and Yorkshire      0
## 455   2020-03-05 North East and Yorkshire      0
## 456   2020-03-06 North East and Yorkshire      0
## 457   2020-03-07 North East and Yorkshire      0
## 458   2020-03-08 North East and Yorkshire      0
## 459   2020-03-09 North East and Yorkshire      0
## 460   2020-03-10 North East and Yorkshire      0
## 461   2020-03-11 North East and Yorkshire      0
## 462   2020-03-12 North East and Yorkshire      0
## 463   2020-03-13 North East and Yorkshire      0
## 464   2020-03-14 North East and Yorkshire      0
## 465   2020-03-15 North East and Yorkshire      2
## 466   2020-03-16 North East and Yorkshire      3
## 467   2020-03-17 North East and Yorkshire      1
## 468   2020-03-18 North East and Yorkshire      2
## 469   2020-03-19 North East and Yorkshire      6
## 470   2020-03-20 North East and Yorkshire      5
## 471   2020-03-21 North East and Yorkshire      6
## 472   2020-03-22 North East and Yorkshire      7
## 473   2020-03-23 North East and Yorkshire      9
## 474   2020-03-24 North East and Yorkshire      8
## 475   2020-03-25 North East and Yorkshire     18
## 476   2020-03-26 North East and Yorkshire     21
## 477   2020-03-27 North East and Yorkshire     28
## 478   2020-03-28 North East and Yorkshire     35
## 479   2020-03-29 North East and Yorkshire     38
## 480   2020-03-30 North East and Yorkshire     64
## 481   2020-03-31 North East and Yorkshire     60
## 482   2020-04-01 North East and Yorkshire     67
## 483   2020-04-02 North East and Yorkshire     75
## 484   2020-04-03 North East and Yorkshire    100
## 485   2020-04-04 North East and Yorkshire    105
## 486   2020-04-05 North East and Yorkshire     92
## 487   2020-04-06 North East and Yorkshire     96
## 488   2020-04-07 North East and Yorkshire    102
## 489   2020-04-08 North East and Yorkshire    107
## 490   2020-04-09 North East and Yorkshire    111
## 491   2020-04-10 North East and Yorkshire    117
## 492   2020-04-11 North East and Yorkshire     98
## 493   2020-04-12 North East and Yorkshire     84
## 494   2020-04-13 North East and Yorkshire     94
## 495   2020-04-14 North East and Yorkshire    107
## 496   2020-04-15 North East and Yorkshire     96
## 497   2020-04-16 North East and Yorkshire    103
## 498   2020-04-17 North East and Yorkshire     88
## 499   2020-04-18 North East and Yorkshire     95
## 500   2020-04-19 North East and Yorkshire     88
## 501   2020-04-20 North East and Yorkshire    100
## 502   2020-04-21 North East and Yorkshire     76
## 503   2020-04-22 North East and Yorkshire     84
## 504   2020-04-23 North East and Yorkshire     63
## 505   2020-04-24 North East and Yorkshire     72
## 506   2020-04-25 North East and Yorkshire     69
## 507   2020-04-26 North East and Yorkshire     65
## 508   2020-04-27 North East and Yorkshire     65
## 509   2020-04-28 North East and Yorkshire     57
## 510   2020-04-29 North East and Yorkshire     69
## 511   2020-04-30 North East and Yorkshire     57
## 512   2020-05-01 North East and Yorkshire     64
## 513   2020-05-02 North East and Yorkshire     48
## 514   2020-05-03 North East and Yorkshire     40
## 515   2020-05-04 North East and Yorkshire     49
## 516   2020-05-05 North East and Yorkshire     40
## 517   2020-05-06 North East and Yorkshire     51
## 518   2020-05-07 North East and Yorkshire     45
## 519   2020-05-08 North East and Yorkshire     42
## 520   2020-05-09 North East and Yorkshire     44
## 521   2020-05-10 North East and Yorkshire     40
## 522   2020-05-11 North East and Yorkshire     29
## 523   2020-05-12 North East and Yorkshire     27
## 524   2020-05-13 North East and Yorkshire     28
## 525   2020-05-14 North East and Yorkshire     31
## 526   2020-05-15 North East and Yorkshire     32
## 527   2020-05-16 North East and Yorkshire     35
## 528   2020-05-17 North East and Yorkshire     26
## 529   2020-05-18 North East and Yorkshire     30
## 530   2020-05-19 North East and Yorkshire     27
## 531   2020-05-20 North East and Yorkshire     22
## 532   2020-05-21 North East and Yorkshire     33
## 533   2020-05-22 North East and Yorkshire     22
## 534   2020-05-23 North East and Yorkshire     18
## 535   2020-05-24 North East and Yorkshire     26
## 536   2020-05-25 North East and Yorkshire     21
## 537   2020-05-26 North East and Yorkshire     21
## 538   2020-05-27 North East and Yorkshire     22
## 539   2020-05-28 North East and Yorkshire     21
## 540   2020-05-29 North East and Yorkshire     25
## 541   2020-05-30 North East and Yorkshire     20
## 542   2020-05-31 North East and Yorkshire     20
## 543   2020-06-01 North East and Yorkshire     17
## 544   2020-06-02 North East and Yorkshire     23
## 545   2020-06-03 North East and Yorkshire     23
## 546   2020-06-04 North East and Yorkshire     17
## 547   2020-06-05 North East and Yorkshire     18
## 548   2020-06-06 North East and Yorkshire     21
## 549   2020-06-07 North East and Yorkshire     14
## 550   2020-06-08 North East and Yorkshire     11
## 551   2020-06-09 North East and Yorkshire     12
## 552   2020-06-10 North East and Yorkshire     19
## 553   2020-06-11 North East and Yorkshire      7
## 554   2020-06-12 North East and Yorkshire      9
## 555   2020-06-13 North East and Yorkshire     10
## 556   2020-06-14 North East and Yorkshire     11
## 557   2020-06-15 North East and Yorkshire      9
## 558   2020-06-16 North East and Yorkshire     10
## 559   2020-06-17 North East and Yorkshire      9
## 560   2020-06-18 North East and Yorkshire     11
## 561   2020-06-19 North East and Yorkshire      6
## 562   2020-06-20 North East and Yorkshire      5
## 563   2020-06-21 North East and Yorkshire      4
## 564   2020-06-22 North East and Yorkshire      7
## 565   2020-06-23 North East and Yorkshire      7
## 566   2020-06-24 North East and Yorkshire     10
## 567   2020-06-25 North East and Yorkshire      4
## 568   2020-06-26 North East and Yorkshire      7
## 569   2020-06-27 North East and Yorkshire      3
## 570   2020-06-28 North East and Yorkshire      5
## 571   2020-06-29 North East and Yorkshire      2
## 572   2020-06-30 North East and Yorkshire      6
## 573   2020-07-01 North East and Yorkshire      1
## 574   2020-07-02 North East and Yorkshire      4
## 575   2020-07-03 North East and Yorkshire      4
## 576   2020-07-04 North East and Yorkshire      4
## 577   2020-07-05 North East and Yorkshire      2
## 578   2020-07-06 North East and Yorkshire      2
## 579   2020-07-07 North East and Yorkshire      3
## 580   2020-07-08 North East and Yorkshire      3
## 581   2020-07-09 North East and Yorkshire      0
## 582   2020-07-10 North East and Yorkshire      3
## 583   2020-07-11 North East and Yorkshire      1
## 584   2020-07-12 North East and Yorkshire      4
## 585   2020-07-13 North East and Yorkshire      1
## 586   2020-07-14 North East and Yorkshire      1
## 587   2020-07-15 North East and Yorkshire      2
## 588   2020-07-16 North East and Yorkshire      2
## 589   2020-07-17 North East and Yorkshire      1
## 590   2020-07-18 North East and Yorkshire      2
## 591   2020-07-19 North East and Yorkshire      2
## 592   2020-07-20 North East and Yorkshire      1
## 593   2020-07-21 North East and Yorkshire      1
## 594   2020-07-22 North East and Yorkshire      4
## 595   2020-07-23 North East and Yorkshire      0
## 596   2020-07-24 North East and Yorkshire      1
## 597   2020-07-25 North East and Yorkshire      1
## 598   2020-07-26 North East and Yorkshire      1
## 599   2020-07-27 North East and Yorkshire      0
## 600   2020-07-28 North East and Yorkshire      2
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## 602   2020-03-02               North West      0
## 603   2020-03-03               North West      0
## 604   2020-03-04               North West      0
## 605   2020-03-05               North West      1
## 606   2020-03-06               North West      0
## 607   2020-03-07               North West      0
## 608   2020-03-08               North West      1
## 609   2020-03-09               North West      0
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## 611   2020-03-11               North West      0
## 612   2020-03-12               North West      2
## 613   2020-03-13               North West      3
## 614   2020-03-14               North West      1
## 615   2020-03-15               North West      4
## 616   2020-03-16               North West      2
## 617   2020-03-17               North West      4
## 618   2020-03-18               North West      6
## 619   2020-03-19               North West      7
## 620   2020-03-20               North West     10
## 621   2020-03-21               North West     11
## 622   2020-03-22               North West     13
## 623   2020-03-23               North West     15
## 624   2020-03-24               North West     21
## 625   2020-03-25               North West     21
## 626   2020-03-26               North West     29
## 627   2020-03-27               North West     36
## 628   2020-03-28               North West     28
## 629   2020-03-29               North West     46
## 630   2020-03-30               North West     67
## 631   2020-03-31               North West     52
## 632   2020-04-01               North West     86
## 633   2020-04-02               North West     96
## 634   2020-04-03               North West     95
## 635   2020-04-04               North West     98
## 636   2020-04-05               North West    102
## 637   2020-04-06               North West    100
## 638   2020-04-07               North West    135
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## 642   2020-04-11               North West    138
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## 644   2020-04-13               North West    129
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## 646   2020-04-15               North West    114
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## 648   2020-04-17               North West     98
## 649   2020-04-18               North West    113
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## 651   2020-04-20               North West     83
## 652   2020-04-21               North West     76
## 653   2020-04-22               North West     86
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## 655   2020-04-24               North West     66
## 656   2020-04-25               North West     66
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## 662   2020-05-01               North West     45
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## 669   2020-05-08               North West     42
## 670   2020-05-09               North West     31
## 671   2020-05-10               North West     42
## 672   2020-05-11               North West     35
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## 674   2020-05-13               North West     25
## 675   2020-05-14               North West     26
## 676   2020-05-15               North West     33
## 677   2020-05-16               North West     32
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## 679   2020-05-18               North West     31
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## 681   2020-05-20               North West     27
## 682   2020-05-21               North West     27
## 683   2020-05-22               North West     26
## 684   2020-05-23               North West     31
## 685   2020-05-24               North West     26
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## 687   2020-05-26               North West     27
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## 690   2020-05-29               North West     20
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## 692   2020-05-31               North West     13
## 693   2020-06-01               North West     12
## 694   2020-06-02               North West     27
## 695   2020-06-03               North West     22
## 696   2020-06-04               North West     22
## 697   2020-06-05               North West     16
## 698   2020-06-06               North West     26
## 699   2020-06-07               North West     20
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## 701   2020-06-09               North West     17
## 702   2020-06-10               North West     16
## 703   2020-06-11               North West     16
## 704   2020-06-12               North West     11
## 705   2020-06-13               North West     10
## 706   2020-06-14               North West     15
## 707   2020-06-15               North West     16
## 708   2020-06-16               North West     15
## 709   2020-06-17               North West     13
## 710   2020-06-18               North West     14
## 711   2020-06-19               North West      7
## 712   2020-06-20               North West     11
## 713   2020-06-21               North West      8
## 714   2020-06-22               North West     11
## 715   2020-06-23               North West     13
## 716   2020-06-24               North West     13
## 717   2020-06-25               North West     15
## 718   2020-06-26               North West      6
## 719   2020-06-27               North West      7
## 720   2020-06-28               North West      9
## 721   2020-06-29               North West      9
## 722   2020-06-30               North West      7
## 723   2020-07-01               North West      3
## 724   2020-07-02               North West      6
## 725   2020-07-03               North West      7
## 726   2020-07-04               North West      4
## 727   2020-07-05               North West      6
## 728   2020-07-06               North West      9
## 729   2020-07-07               North West      8
## 730   2020-07-08               North West      5
## 731   2020-07-09               North West     10
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## 742   2020-07-20               North West      0
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## 745   2020-07-23               North West      2
## 746   2020-07-24               North West      1
## 747   2020-07-25               North West      0
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## 772   2020-03-22               South East     25
## 773   2020-03-23               South East     20
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## 775   2020-03-25               South East     29
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## 783   2020-04-02               South East     55
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## 811   2020-04-30               South East     29
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## 816   2020-05-05               South East     29
## 817   2020-05-06               South East     25
## 818   2020-05-07               South East     27
## 819   2020-05-08               South East     26
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## 822   2020-05-11               South East     25
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## 958   2020-04-27               South West     13
## 959   2020-04-28               South West     17
## 960   2020-04-29               South West     15
## 961   2020-04-30               South West     26
## 962   2020-05-01               South West      6
## 963   2020-05-02               South West      7
## 964   2020-05-03               South West     10
## 965   2020-05-04               South West     17
## 966   2020-05-05               South West     14
## 967   2020-05-06               South West     19
## 968   2020-05-07               South West     16
## 969   2020-05-08               South West      6
## 970   2020-05-09               South West     11
## 971   2020-05-10               South West      5
## 972   2020-05-11               South West      8
## 973   2020-05-12               South West      7
## 974   2020-05-13               South West      7
## 975   2020-05-14               South West      6
## 976   2020-05-15               South West      4
## 977   2020-05-16               South West      4
## 978   2020-05-17               South West      6
## 979   2020-05-18               South West      4
## 980   2020-05-19               South West      6
## 981   2020-05-20               South West      1
## 982   2020-05-21               South West      9
## 983   2020-05-22               South West      6
## 984   2020-05-23               South West      6
## 985   2020-05-24               South West      3
## 986   2020-05-25               South West      8
## 987   2020-05-26               South West     11
## 988   2020-05-27               South West      5
## 989   2020-05-28               South West     10
## 990   2020-05-29               South West      7
## 991   2020-05-30               South West      3
## 992   2020-05-31               South West      2
## 993   2020-06-01               South West      7
## 994   2020-06-02               South West      2
## 995   2020-06-03               South West      7
## 996   2020-06-04               South West      2
## 997   2020-06-05               South West      2
## 998   2020-06-06               South West      1
## 999   2020-06-07               South West      3
## 1000  2020-06-08               South West      3
## 1001  2020-06-09               South West      0
## 1002  2020-06-10               South West      1
## 1003  2020-06-11               South West      2
## 1004  2020-06-12               South West      2
## 1005  2020-06-13               South West      2
## 1006  2020-06-14               South West      0
## 1007  2020-06-15               South West      2
## 1008  2020-06-16               South West      2
## 1009  2020-06-17               South West      0
## 1010  2020-06-18               South West      0
## 1011  2020-06-19               South West      0
## 1012  2020-06-20               South West      2
## 1013  2020-06-21               South West      0
## 1014  2020-06-22               South West      1
## 1015  2020-06-23               South West      1
## 1016  2020-06-24               South West      1
## 1017  2020-06-25               South West      0
## 1018  2020-06-26               South West      3
## 1019  2020-06-27               South West      0
## 1020  2020-06-28               South West      0
## 1021  2020-06-29               South West      1
## 1022  2020-06-30               South West      0
## 1023  2020-07-01               South West      0
## 1024  2020-07-02               South West      0
## 1025  2020-07-03               South West      0
## 1026  2020-07-04               South West      0
## 1027  2020-07-05               South West      1
## 1028  2020-07-06               South West      0
## 1029  2020-07-07               South West      0
## 1030  2020-07-08               South West      2
## 1031  2020-07-09               South West      0
## 1032  2020-07-10               South West      1
## 1033  2020-07-11               South West      0
## 1034  2020-07-12               South West      0
## 1035  2020-07-13               South West      1
## 1036  2020-07-14               South West      0
## 1037  2020-07-15               South West      0
## 1038  2020-07-16               South West      0
## 1039  2020-07-17               South West      1
## 1040  2020-07-18               South West      0
## 1041  2020-07-19               South West      0
## 1042  2020-07-20               South West      0
## 1043  2020-07-21               South West      0
## 1044  2020-07-22               South West      0
## 1045  2020-07-23               South West      0
## 1046  2020-07-24               South West      0
## 1047  2020-07-25               South West      0
## 1048  2020-07-26               South West      0
## 1049  2020-07-27               South West      0
## 1050  2020-07-28               South West      0

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2020-07-29"

The completion date of the NHS Pathways data is Wednesday 29 Jul 2020.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##      Min        1Q    Median        3Q       Max  
## -14.9092   -5.3012   -0.6174    3.8783    9.5829  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.452e+00  7.036e-02   63.27   <2e-16 ***
## note_lag    1.572e-05  7.348e-07   21.39   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 30.79853)
## 
##     Null deviance: 15532.0  on 88  degrees of freedom
## Residual deviance:  2880.3  on 87  degrees of freedom
##   (23 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 4

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##   85.772135    1.000016
exp(confint(lag_mod))
##                 2.5 %    97.5 %
## (Intercept) 74.538605 98.221493
## note_lag     1.000014  1.000017

Rsq(lag_mod)
## [1] 0.8145597

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                            sysname 
##                                                                                           "Darwin" 
##                                                                                            release 
##                                                                                           "19.6.0" 
##                                                                                            version 
## "Darwin Kernel Version 19.6.0: Sun Jul  5 00:43:10 PDT 2020; root:xnu-6153.141.1~9/RELEASE_X86_64" 
##                                                                                           nodename 
##                                                                                "Mac-1596103696300" 
##                                                                                            machine 
##                                                                                           "x86_64" 
##                                                                                              login 
##                                                                                             "root" 
##                                                                                               user 
##                                                                                           "runner" 
##                                                                                     effective_user 
##                                                                                           "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin17.0     
## arch           x86_64                      
## os             darwin17.0                  
## system         x86_64, darwin17.0          
## status                                     
## major          4                           
## minor          0.2                         
## year           2020                        
## month          06                          
## day            22                          
## svn rev        78730                       
## language       R                           
## version.string R version 4.0.2 (2020-06-22)
## nickname       Taking Off Again

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 4.0.2 (2020-06-22)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS Catalina 10.15.6
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.1     ggpubr_0.4.0         lubridate_1.7.9     
##  [4] chngpt_2020.5-21     cyphr_1.1.0          DT_0.14             
##  [7] kableExtra_1.1.0     janitor_2.0.1        remotes_2.2.0       
## [10] projections_0.5.1    earlyR_0.0.1         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.2      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.6          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.0        stringr_1.4.0       
## [22] dplyr_1.0.0          purrr_0.3.4          readr_1.3.1         
## [25] tidyr_1.1.0          tibble_3.0.3         ggplot2_3.3.2       
## [28] tidyverse_1.3.0      here_0.1             reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] nlme_3.1-148      fs_1.4.2          webshot_0.5.2     httr_1.4.2       
##  [5] rprojroot_1.3-2   tools_4.0.2       backports_1.1.8   utf8_1.1.4       
##  [9] R6_2.4.1          mgcv_1.8-31       DBI_1.1.0         colorspace_1.4-1 
## [13] withr_2.2.0       gridExtra_2.3     tidyselect_1.1.0  sodium_1.1       
## [17] curl_4.3          compiler_4.0.2    cli_2.0.2         labeling_0.3     
## [21] matchmaker_0.1.1  scales_1.1.1      digest_0.6.25     foreign_0.8-80   
## [25] rmarkdown_2.3     pkgconfig_2.0.3   htmltools_0.5.0   dbplyr_1.4.4     
## [29] htmlwidgets_1.5.1 rlang_0.4.7       readxl_1.3.1      rstudioapi_0.11  
## [33] farver_2.0.3      generics_0.0.2    jsonlite_1.7.0    crosstalk_1.1.0.1
## [37] car_3.0-8         zip_2.0.4         magrittr_1.5      kyotil_2019.11-22
## [41] Matrix_1.2-18     Rcpp_1.0.5        munsell_0.5.0     fansi_0.4.1      
## [45] viridis_0.5.1     abind_1.4-5       lifecycle_0.2.0   stringi_1.4.6    
## [49] yaml_2.2.1        carData_3.0-4     snakecase_0.11.0  MASS_7.3-51.6    
## [53] plyr_1.8.6        grid_4.0.2        blob_1.2.1        crayon_1.3.4     
## [57] lattice_0.20-41   cowplot_1.0.0     splines_4.0.2     haven_2.3.1      
## [61] hms_0.5.3         knitr_1.29        pillar_1.4.6      boot_1.3-25      
## [65] ggsignif_0.6.0    reprex_0.3.0      glue_1.4.1        evaluate_0.14    
## [69] data.table_1.13.0 modelr_0.1.8      vctrs_0.3.2       selectr_0.4-2    
## [73] cellranger_1.1.0  gtable_0.3.0      assertthat_0.2.1  xfun_0.16        
## [77] openxlsx_4.1.5    broom_0.7.0       rstatix_0.6.0     survival_3.1-12  
## [81] viridisLite_0.3.0 ellipsis_0.3.1